Protection as a Commitment Problem

Jason S. Davis, University of Pennsylvania*

August 15, 2019

Abstract

Restrictions on trade are inefficient means of redistributing income compared to a widevariety of alternatives, so why are they used? I develop a dynamic model that demon-strates that commitment problems in the trade-lobbying process can account for this.Many industries that are harmed by open trade have an incentive to lobby for protec-tion over compensatory transfers because liberalization has dynamic effects that canreduce an industry’s future political influence. Thus, while all parties would prefer per-manent transfers to protection, these transfers are subject to a commitment problem.The model also demonstrates that despite this, “compensating the losers” can still be aneffective political strategy under certain scope conditions: even short-term compensationmay disrupt protectionist equilibria. Thus, this paper helps to resolve an outstandingtheoretical puzzle about the inefficiency of trade protection while providing a new in-terpretation of the compromise of “embedded liberalism”, in a fashion that can help toexplain the variation in compensation’s successful use.

IntroductionExisting accounts of protectionism in the political economy literature have tended to focuson the redistributive consequences of trade policies. For instance, this work has addressedthe conditions under which trade-related political divisions will be along factor or industrylines (Rogowski 1989, Scheve and Slaughter 2001, Hiscox 2002, Mayda and Rodrik 2005),and the conditions under which there may be divisions within industries between firms (Os-good 2016, Kim 2017). Broadly, this approach suggests that if the groups that benefit fromtrade protection are more politically influential than those that lose, we should expect gov-ernments to impose restrictions on trade.1

*Browne Center for International Politics. E-mail: jasonsd@sas.upenn.edu.1Related research addresses the factors which determine group influence, including lobbying (Gross-

man and Helpman 1994, Goldberg and Maggi 1999, Gawande and Bandyopadhyay 2000, Bombardini 2008,Gawande et al. 2012), democratization (Mansfield et al. 2000, Milner and Kubota 2005), and more.

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However, if we accept the premise that trade policy is primarily a way of redistributing in-come, it remains unclear why the actors in a redistributive game would choose protection asthe means for redistributing income over any number of alternatives available to the gov-ernment. Indeed, there are strong theoretical reasons to believe that protection should beone of the least attractive options.

Consider that governments generally have many mechanisms for transferring income thatare more efficient than trade protection - tax credits, adjustment assistance, etc. - whichwould increase the “size of the pie” being bargained over. Thus, if these mechanisms wereused instead of protection, it should be possible to completely compensate all groups for anylosses they would suffer under free trade, while generating a surplus that could be allo-cated so as to make all parties better off than they were under protection. This creates ananalogous puzzle to one often discussed about inefficiency of war2 - if Pareto-superior bar-gains are available to the actors in the trade policy game, why do we ever see protectionism?

Further complicating the story is that while governments often fail to compensate the losers,they don’t always. The “embedded liberalism” literature has consistently found empiricalsupport for the idea that governments use compensation in a way that increases support forfreer trade (Ruggie 1982, Hays et al. 2009, Walter 2010, Margalit 2011). However, this lit-erature leaves several questions unaddressed: who are the actors who receive this welfare-based compensation? Under which conditions will this bargain be effective in obtainingfreer-trade, and under which will it falter? What accounts for the highly heterogeneous useof compensation and protection across sectors, industries, states, and time?

I develop a dynamic model that can help address these puzzles. The model identifies thatinterest groups that are harmed by the opening up of trade can have an incentive to lobbyfor protection over compensatory transfers because free-trade has dynamic effects (reducedprofits, shrinking employment, disrupted interest group cohesion, etc.) that reduce a group’sability to lobby the government in future periods. Given this, interest groups that couldinitially extract favorable policy from the government may find they are unable to after themove to free trade. Thus while both parties would prefer permanent compensatory transfersto protectionism, interest groups know that governments will lose the incentive to maintainthese transfers in the future, resulting in a commitment problem.

However, while these dynamic effects make protectionist policies more attractive, they arenot always pivotal in the choices of interest groups. Protection becomes especially costlyfor the government to provide when the good in question is subject to high import demandelasticities (which increase deadweight losses from protection) and high lobby competitionfrom downstream industries (such as when automobile manufacturers lobby against steeltariffs). Moreover, states’ access to alternative means of compensating interest groups canvary (states with high fiscal capacity can do this more easily), and interest groups face dif-

2Fearon 1995, for instance.

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fering degrees of dynamic decline with open trade (some groups may retain most of theirpolitical influence, while some may face complete dissolution in the face of import competi-tion). The model illustrates how compensation may thus still be chosen by interest groupswhen various factors either make protection more costly to obtain or compensation moreattractive.

Consequently, the model can improve our understanding of trade politics in two ways. First,it helps resolve a theoretical puzzle about the inefficiency of protection as a means of re-distributing income: Pareto-improving bargains should exist, but these are not politicallyfeasible due to commitment problems in the trade lobbying process. Second, the modeldevelops an alternative theoretical foundation for embedded liberalism, in a way that canbetter account for its heterogeneity: compensation can indeed be an important part of apolitical bargain obtaining freer trade, but only when states possess sufficient capacity toimplement alternative means of redistribution, and when import competing groups findprotection more costly to obtain than it’s worth (due to high import demand elasticities andpolitical competition, or relatively low prospective rates of political decline).

Existing Arguments on The Inefficiency of ProtectionismWhile the “inefficiency puzzle” of war has proven central to the rationalist conflict litera-ture, the political economy of trade literature has devoted surprisingly little attention toexplaining the choice of trade as a redistributive tool over more efficient means. Grossmanand Helpman (1994) has a paragraph that is dedicated to this question, which argues thatspecial interest groups may benefit from tying the hands of the government. However, theirargument is not formally developed (mostly included as an aside to the main argument),and provides very little scope for protectionism except as an unused “threat” that allowsspecial interest groups to extract greater gains from a bargaining game. Kono (2006) issometimes cited in relation to this question, but it focuses on explaining the move towardsnon-tariff barriers (NTBs) from tariffs, and does not directly address the question of whyprotectionism - whether NTBs or tariffs - would be used over more efficient mechanisms forredistributing income.

Dixit and Londregan (1995) addresses a related question - how redistribution can lead to in-efficiency - with a distributive politics model that argues that voters that have advantageouspolitical characteristics (e.g. swing voters) may make inefficient decisions if doing so allowsthem to retain these characteristics. For instance, voters in politically pivotal flood-proneareas may decide not to move to avoid losing redistributive transfers. However, the modeldoes not address why the form of redistribution would be inefficient; indeed, transfers areexplicitly modeled as efficient and lump-sum (Dixit and Londregan 1995, p.858).

Some explanations for the phenomenon of inefficient redistribution exist in the politicaleconomy literature more generally (e.g. Coate and Morris 1995, Acemoglu 2003, Drazenand Limao 2008), ranging from bargaining models to information asymmetries, but none of

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these have been applied to international trade specifically. Acemoglu and Robinson (2001)comes closest; it argues industries might favor inefficient redistribution if it increases theirsize and correspondingly their political influence, and while the paper primarily focuses onfarm subsidies and labor market policy, it briefly discusses how the model might apply tointernational trade. Their paper provides valuable insights, but the model is not a naturalfit with trade. For instance, the main factor determining whether inefficient redistributionoccurs is whether absolute rents increase quickly enough with group size in order to lead toan increase in per capita rents for the farmers who are around at the beginning of the game;with trade protection, per capita rents are likely always increasing, so this should alwaysbe satisfied, allowing very little scope for open trade. Similarly, their model generates com-parative statics about factor specificity that are hard to square with the trade literature:they argue that high factor mobility might lead to more inefficient redistribution, while thetrade literature suggests that high factor mobility shifts the political cleavages associatedwith protection from industry to factor lines (why would farmers have an incentive to switchindustries if their returns are not diminished?).

In contrast, this paper seeks to address how commitment problems arise with trade in par-ticular, by building off of trade theory more directly and using an approach to modelinglobbying in trade that is more consistent with the trade literature (i.e. a menu-auction).This allows the model to generate comparative statics relating to measurable trade param-eters (like import demand elasticities) and other factors considered important by the tradeliterature (like competition from downstream industries) (Gawande et al. 2012).

Embedded LiberalismFurthermore, while the broader political economy literature has outlined some explanationsfor inefficient redistribution, these models have generally provided less insight into whenwe might expect efficient redistribution instead. This project’s model, in contrast, predictsboth types of redistribution, allowing the paper to speak to the literature on “embeddedliberalism”, which broadly argues for a compensation story in which government spendingcan be a means of blunting opposition to openness from trade’s losers. This literature beganby arguing that the post-war expansion of the welfare state was an important example ofthis kind of compensation (Ruggie 1982). Rodrik 1998 brought statistical evidence to bearon this question, identifying a correlation between public sector size and external openness.Later work has continued to find empirical support for the hypothesis that compensationprograms can be used to increase support for open trade, using data from trade adjustmentassistance in the United States (Margalit 2011, Ritchie and You forthcoming), active labormarket programs in the OECD (Hays et al. 2005, Hays 2009), and even survey experiments(Ehrlich and Hearn 2014).

While this literature has usefully demonstrated that compensation can be an important partof political bargains on trade, it generally has not explored in depth the conditions underwhich such compensation should be helpful, or which groups are most likely to be success-

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ful in obtaining compensation. Moreover, in the wake of the “anti-globalization backlash”reflected in Brexit, the election of Donald Trump, and the rise of Marine Le Pen’s NationalFront/Rally, there has been renewed interest amongst IPE scholars in these kinds of ques-tions, as many have sought to understand why embedded liberalism failed to prevent thisbacklash (see, for instance, Mansfield and Rudra n.d.).

This paper provides an alternative theoretical framework for embedded liberalism that canbe useful in answering these questions. Historically, the underlying theory assumed in theembedded liberalism literature has been that compensation is a means of ensuring againstincome volatility generated by external openness (Rodrik 1998, Burgoon 2001, Rudra 2002).This has proved to be inconsistent with a number of empirical regularities identified bytrade scholars - most importantly, that it is not at all clear that openness increases volatil-ity (Kim 2007, Gray and Potter 2012). The literature has also demonstrated that greateropenness is associated with less government spending on social welfare in the developingworld (Rudra 2002, Wibbels and Ahlquist 2011), which is difficult to square with a theory ofcompensation in which all states seek to reduce income volatility via social spending.

This paper’s model instead adopts a more straightforward conception of embedded liber-alism; that it is a compensatory bargain between import-competing actors and the gov-ernment. This framework is consistent with the existing evidence, as there is no need todemonstrate a link between openness and volatility, and we would not expect trade-relatedcompensation to target the recipients of social welfare in developing countries, given thatthe “losers” of trade in developing countries are more likely to be high-skilled workers (Ro-gowski 1989, Maydra and Rodrik 2005). Indeed, Nooruddin and Rudra (2014) find thatdeveloping countries are able to compensate some of the losers of trade by increasing publicsector employment, with these jobs going to an elite class of workers.3

However, if we assume that embedded liberalism is a bargain, then explanations for its suc-cess and failure must be rooted in some understanding of this bargaining process. It is notsufficient, for instance, to simply explain why certain actors may have come to find trademore or less attractive, or to explain why the actors that oppose trade may have becomemore politically powerful; instead, we need to explain when the groups that oppose tradecan be “bought off” by those that benefit, and when they cannot.

This paper contributes to our understanding of embedded liberalism by providing a modelthat predicts both that compensation will often be effective, and that it will often fail, withan explanation for embedded liberalism’s limitations rooted in a theory of bargaining fail-ure. This contrasts with existing explanations for the failure of embedded liberalism thatfocus on factors such as the development of global value chains, changes in technology, or

3Rickard (2012) argues that developing countries adopt compensatory strategies which deemphasize wel-fare spending in favor of more targeted production subsides, but those subsidies end up performing a similarfunction to tariffs in propping up import-competing industries, and should thus not be treated as a compen-satory alternative to protection.

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the rising discontent of unskilled workers left behind by globalization (Frieden 2018, Owen2019, Mansfield and Rudra n.d.), which fundamentally explain why the need for compen-satory bargains may have increased over time, but do not explain why those bargains failedto materialize.

Moreover, this paper’s model can help to explain the broader patterns of compensation andprotection across states, sectors, industries, and time. For instance, the partial reversal ofthe embedded liberalism welfare state bargain in the 1980s can be attributed to dynamics;if the groups that were being compensated via the welfare state had become weaker overtime, the incentives to maintain the size of the welfare state would naturally have dissi-pated. More generally, the model provides a set of characteristics that circumscribe theconditions under which compensation can be a politically efficient strategy, allowing us abetter understanding of when we should expect to observe it instead of protection.

Trade DynamicsThroughout the political science literature, and particularly in the study of conflict, we haveseen that dynamics can lead to inefficient policy.4 However, despite the importance of dy-namics in these other domains, the trade literature has largely treated the policymakinggame as static5, when we might realistically expect interest groups to be forward-lookingand subject to change over time in both capacities and interests.

This project models the process of liberalization as leading deterministically to a reductionin the political influence of protectionist lobby groups, and argues that it is impossible todevise a policy that fully compensates these protectionist groups and maintains their politi-cal influence without sacrificing the gains associated with freer trade. The reason for this isthat the dynamic effects that weaken protectionist interest groups arise from the very na-ture of the economic changes that need to occur in order for liberalization to generate thesegains. Consider, first, a subsidy policy designed to prop-up the trade-threatened industry.This policy would likely have the desired effect of redistributing income to the protectionistgroup, but the main benefits of trade arise when inputs are allowed to relocate from compar-ative disadvantaged sectors to comparative advantaged sectors. This requires the decline ofthe comparative disadvantage industry; if subsidies are used to prevent this decline, theyare performing a similar function as other protectionist measures.

Now consider an alternative compensation policy, where the government provides incometransfers to the individuals associated with a particular industry, but does not tie thesetransfers to those individuals remaining in the industry. This can be conceptualized aspaying these workers to leave the industry so that the process of greater specialization inthe face of trade competition can occur. This approach achieves the full gains of trade, but

4Powell (2004, 2006) discuss this in relation to conflict.5Bailey et. al. 1997, Hathaway 1998 are exceptions.

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necessarily leads to shrinking size of the industry as workers leave to find employment inother industries, reductions of the producer surpluses of the import-competing firms, and ashifting firm-composition towards exporting firms within import-competing industries. Inthe most extreme case, this can lead to what amounts to the total dissolution of the indus-try. In contrast, any domestic interest groups that benefit from trade liberalization growin size, and obtain higher producer surpluses. All of these economic changes have politicalimplications.

To start, insofar as the protectionist interest group is organized around an industry, havingfewer members is likely to reduce its political influence. Large interest groups tend to bemore influential than smaller ones, ceteris paribus (Chong and Gradstein 2010). Second, ifthe producer surplus of the industry is reduced, the lobby group retains fewer resourceswith which to make political contributions or fund lobbying activity, particularly if thisgroup faces credit-constraints. Third, because of the shifting firm-composition within anindustry, the remaining firms will tend to be weighted towards those that are less resistantto trade. Fourth, because any pro-trade interest groups experience the converse economiceffects, a protectionist group now faces greater competition if they try to lobby for a returnto protectionist policies. Thus, liberalization can create “lock-in”, where it becomes morechallenging to reverse the process once it has begun, while pro-protectionist lobby groupsare weakened in their ability to obtain any kind of policy concession, trade-related or not.

Could compensating income transfers to the trade-distressed workers be used as resourceswith which to lobby the government for compensation? This is unlikely, for two reasons.Before liberalization had occurred, these workers were part of an organized industry thathad, ostensibly, solved the collective action problem associated with lobbying the govern-ment. However, if workers have dispersed into several industries, it becomes much morechallenging to continue to organize them in a cohesive fashion. Moreover, insofar as eachworker is now part of some new, industry-level lobby, they are likely to be too small a pro-portion of this other special interest group for it to have an incentive to lobby to maintaincompensation.

Secondly, the differing character of compensation transfers versus protectionist rents maylead to greater fractionalization amongst those lobbying for continued compensation. Whileprotectionism is inherently a collective good, and thus can create incentives to lobby as agroup (though the size of the group can vary based on industry characteristics and tariffspecificity), compensation is a private transfer that can be provided to one part of the groupbut not the other. For instance, say an industry declines, and some percentage of the exit-ing workers find employment and some percentage do not; might this not create divisionsbetween the newly unemployed and the newly employed, where the unemployed might notlobby so hard for transfers to be maintained for those who have found employment? Frac-tures within the group would lead to weakening of the political interest group as a whole.

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It is also worth considering whether industries facing distress become more politically influ-ential. It may sometimes appear that this is the case, as distressed industries are often ableto obtain the most obvious concessions;6 however, this likely conflates greater preferences forprotection with greater ability to wield power to obtain concessions. Special interest groupsthat are distressed by foreign competition would naturally invest more resources in lobby-ing for protection, as the gains of obtaining it are higher (an industry that is not distressedis likely at a comparative advantage, and thus has less to gain from higher tariffs). How-ever, variation on this dimension is unrelated to whether or not the group is more politicallypowerful - it simply affects how visible that influence is. In any event, this paper explicitlycompare apples to apples by considering an industry that is already threatened by foreigncompetition and what happens if liberalization occurs. Under these circumstances, politicalinfluence is strictly declining as the industry declines with greater liberalization.

While liberalization reduces the influence of import-competing groups, the degree that in-fluence declines is not equal across interest groups. Some groups face steeper declines thanothers, for a variety of reasons including firm heterogeneity, access to alternative produc-tion technologies, political geography, and more. I do not develop a model explaining thevariation in dynamic decline in this paper (though I think this would be an exciting areafor future inquiry), but I do analyze some specific cases with an eye to how variation in thisdimension can condition choices between protection and compensation.

Model

SetupThe model outlined in this paper is a political support menu-auction model similar to Gross-man and Helpman’s Protection for Sale, in which two industry-level special interest groups(SIGs) compete to influence an incumbent government (SIGs are principals and the govern-ment is the agent). One SIG is the main import-competing “upstream” industry (SIG 1) thatbenefits from protection, while the other is a “downstream” industry (SIG 2) that prefersliberalization of the good in question (e.g. steel producers as an “upstream” industry andautomobile manufacturers as a “downstream” industry). Thus, they have opposite prefer-ences over the tariff rate τ, due to how it affects the price of some good.

The upstream SIG also has preferences over compensation R via some other, more effi-cient redistributive instrument. The downstream SIG is indifferent between levels of R; itis assumed that compensation does not affect the price of the good (which is true for themost efficient forms of transfers), and is functionally noncompetitive. While governmentsinevitably have to make trade-offs in deciding which groups to compensate from budgetaryrevenues, if there are a sufficiently large number of interest groups it seems likely that

6Baldwin and Robert-Nicoud (2007) surveys the economics literature addressing this question, noting sev-eral empirical regularities such as higher tariff rates in recessions.

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groups would not see their interests as conflictual enough that they would actively lobbyagainst another’s transfers. The two SIG setup accounts for competition between specialinterest groups while remaining tractable.

These SIGs attempt to influence a government that is maximizing a weighted sum of voterwelfare and lobby contributions, where contributions may mean literal contributions, butmay also mean expenses by a lobby in service of a particular government. “Voter welfare”simply means the aggregate economic performance of the country as a whole. For simplic-ity, I assume that the upstream lobby has to choose whether to pursue only protectionismor only compensation via the more efficient redistributive instrument. This also focuses at-tention on the main comparison of interest to this paper.

Importantly, I assume that the dynamics described earlier lead to a reduction in politicalinfluence for the import-competing industry, but I do not explicitly model the source of thesedynamics. This is by design: given that there are multiple mechanisms by which influencedecreases with increased liberalization, and all the effects are in the same direction, I be-lieve the assumption that there is a reduction in political influence is easier to justify thanany particular formulation. I do, however, include a parameter in the model for the degreeof dynamic decline, as this varies across interest groups - some face steeper declines withliberalization than others - in ways that matter for the equilibria generated by the model.

The game proceeds as follows:

1. Game begins in a state of protectionism, i.e. St = P.

2. SIG 1 chooses whether to pursue protection or compensation, i.e. chooses T ∈ 0,1,where T = 0 means compensation and T = 1 means protection.

3. If T = 0, the tariff rate defaults to zero (τ= 0), so SIG 2 obtains their preferred outcomewithout lobbying. SIG 1 then chooses what contributions to “bid” to the governmentin exchange for compensation R. If T = 1, both SIG 1 and SIG 2 set contributionschedules to try to influence the government.

4. Government chooses R ∈ [0,∞) or τ ∈ [0,∞) depending on T and obtains the contribu-tions defined by the schedules.

5. Period payoffs realized. If T = 1, the state of the world remains protectionist, andthe game repeats from stage 1. If T = 0, the game transitions to a state of free trade(St = F), such that the import-competing interest group (SIG 1) experiences a declinein political influence. This is an absorbing state: there is no way to exit the free tradestate once it is reached.7

7This is a simplification. The substantively important aspect of this assumption is that there is some degreeof influence that is lost once trade is liberalized that cannot be regained. A version of the model with thisassumption relaxed is included in the appendix.

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St = P,F is the state space at time t, R can take on any positive real number, and τ isbounded by zero below, so we rule out import subsidies. C1 and C2 represent the amount ofcontributions made by SIG 1 and SIG 2 respectively. The reduction in political influence isparameterized by a movement from ψP to ψF , with ψF > ψP ; this parameter is a positivereal number (ψs ∈ R+) that captures how costly making lobbying contributions is for SIG 1(or equivalently, the efficiency of their contributions). This conceptualization fits naturallywith how trade dynamics were described earlier in the paper: insofar as liberalization re-duces industry profits and disrupts the organization and cohesiveness of interest groups,one would expect it to become more “costly” to make the same level of contribution as priorto liberalization. As a concrete example: having lower profits implies that contributions orother expenses will need to come via other sources, which may mean borrowing, divertingfrom research spending, etc. - these other means may impose higher costs than redirectingprofits.

This setup leads to the following objective functions for any single period of the game.

• SIG 1: u1(τ,R,T,St)= Tπ1(τ)+ (1−T)(R+π1(0))−ψsC1(τ,R)

• SIG 2: u2(τ)= X +βπ2(τ)−C2(τ)

• Government: G = C1(τ,R)+C2(τ)+αW(τ,R,ε,ρ)

Where β ∈ [0,∞) parameterizes the degree of lobby competition from a downstream indus-try. If β = 0, there is no competition, and SIG 2 obtains only income exogeneous to themodel, X . If β > 0, this ensures that some share (βπ2(τ)) of SIG 2’s income is impacted byτ, with ∂π2

∂τ< 0. Thus, at higher β, τ has a higher impact on SIG 2’s income, which captures

naturally the idea of conflictual interests between the two groups.

Meanwhile, SIG 1 always benefits from increases in τ, i.e. ∂π1∂τ

> 0. This follows straightfor-wardly from the fact that one SIG is upstream and the other is downstream; SIG 1 gainsfrom having their good protected, but SIG 2 loses from facing higher prices of some in-put in their production process. Furthermore, both π1 and π2 are concave functions, i.e.∂2π1∂τ2 < 0, ∂2π2

∂τ2 < 0. This is a natural assumption: early increases in τ provide a significantcompetitive advantage, while at some point, later increases in τ will have shut out all for-eign competition leading to prices determined by domestic market conditions.

Voter welfare W is decreasing in both R and τ, and is concave in each.8 α is the weightingplaced on voter welfare by the government. Import demand elasticity ε has a conditioningeffect on the rate that W decreases with τ, i.e. ∂2W

∂τ∂ε< 0. This follows straightforwardly from

8This rules out “optimal tariffs”, which exist when a large country with sufficient market share can gainby imposing a tariff that improves their terms of trade (though this reduces global efficiency). Bagwell andStaiger 2002 provide an account that takes these seriously, discussing how terms-of-trade externalities mightbe resolved through reciprocal trade agreements. However, insofar as such agreements succeed in resolvingterms-of-trade issues, protection is once again strictly welfare decreasing.

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economic theory: if an industry faces a high import demand elasticity, then small changesin the price of a good have greater effects on consumption decisions, and thus tariffs willgenerate larger deadweight losses for the economy imposing a tariff. In contrast, a perfectlyinelastic industry will produce no deadweight losses from tariff-based changes to the price,as this will not distort consumption decisions, and will simply result in a transfer in in-come from consumers to the government (the exporting industry increases the price by theamount of the tariff, but since the same amount is imported, the burden falls entirely on theimporters while the government collects the tax revenue). Note as well that W is strictlydecreasing in τ, which implies that ∂W

∂ε(τ)< 0 at any τ> 0, and ∂W

∂ε(τ)= 0 at τ= 0.

Fiscal capacity ρ has a similar (but opposite) conditioning effect on the rate that W decreaseswith R, i.e. ∂2W

∂R∂ρ > 0, ∂W∂ρ

> 0 at any R > 0 and ∂W∂ρ

= 0 at R = 0 . Here, fiscal capacity isconceived of as the degree of efficiency of the alternative instrument. Countries with higherfiscal capacity have better non-tariff instruments for redistributing income; they may, forinstance, have tax credits, trade adjustment assistance, etc. that can be used to redistributeincome at relatively low cost. In contrast, low fiscal capacity countries may have fewermeans of generating revenues besides tariffs, such that any compensation ends up beinghighly distortionary as well. The model allows for variation in this dimension, but makesthe following assumption:

Assumption 1. For any tariff rate τ′, with R′ =π1(τ′)−π1(0), it is the case that W(0,0,ε,ρ)−W(τ′,0,ε,ρ)>W(0,0,ε,ρ)−W(0,R′,ε,ρ), for all ε and ρ

This is the foundational assumption that compensation is a more efficient way of redis-tributing income than tariffs, though the degree of difference between the two instrumentsis conditioned by ε and ρ. This assumption is not usually very controversial, as given anearly infinite set of possible things to tax in order to redistribute income, it seems unlikelythat trade tariffs or non-tariff barriers are the most efficient option.9 However, there is alsowork in the trade literature that addresses this question in detail (for instance, Dixit 1985).If this assumption did not hold, as might plausibly be argued for the case of less-developedcountries with limited fiscal capacity, then the equilibrium outcome of the model is imme-diately clear: tariffs would always be chosen, as they are then the most efficient means ofredistributing income and the means that best retains the political influence of the groupsthat receive it. This paper is not primarily interested in these cases, which I suspect makeup (at most) a very small percentage of the total.

AnalysisWe can now move on to an equilibrium analysis of the model. We start by examining whatwill happen if SIG 1 chooses to pursue protection. In equilibrium, given that SIG 1 is thefirst mover, they are effectively able to choose the τ that will eventually be implemented bytaking into account in advance what SIG 2 and the Government will do in response. Thus

9This conclusion is strengthened when one considers reciprocal responses to trade protection.

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we need to characterize their optimal τ.

In this case, given the sequencing of the game and full information, SIG 1 offers to con-tribute an amount in exchange for their chosen tariff rate that exactly compensates the gov-ernment for both the weighted costs to voter welfare, and the foregone contributions fromSIG 2. SIG 2 offers a schedule in which contributions exactly equal the benefit they wouldderive from lowering the tariff; in other words, their contribution schedule is “truthful”,in the sense described by Bernheim and Whinston (1986).10 Some non-truthful contribu-tion schedules are possible in equilibrium, but only if they produce the same result as thetruthful schedule, and truthful strategies are weakly dominant - thus I restrict attentionto truthful schedules.11 Government’s only sequentially rational strategy is to choose thetariff rate that maximizes their weighted sum of contributions and voter welfare, which inequilibrium means they accept SIG 1’s offer and implement the tariff level requested.

To see the intuition of this, note that SIG 2 is aware of Government’s objective function andthus chooses a contribution schedule with full information about what tariff rate will beimplemented in response to it, having already observed SIG 1’s schedule. SIG 1 has no in-centive to offer higher contributions than in the strategy profile outlined above, as they areobtaining their chosen tariff rate. If they, instead, offer a lower contribution, they will notachieve their chosen tariff outcome, as SIG 2 will exploit the gap by offering a contributionlevel that makes Government prefer implementing a lower tariff than what SIG 1 chose.Thus, SIG 1 chooses τ to maximize their objective function, taking into account that theywill need to pay for SIG 2’s foregone contributions and the cost of the welfare distortion tothe Government.12

Thus we have:

u1(τ,St|T = 1,R = 0)=π1(τ)−ψs((αW(0,0,ε,ρ)−αW(τ,0,ε,ρ))+ (X +βπ2(0)− (X +βπ2(τ)))=π1(τ)+ψs(αW(τ,0,ε,ρ)+βπ2(τ)−αW(0,0,ε,ρ)−βπ2(0))

The above gives SIG 1’s objective function, where they take into account SIG 2 and theGovernment’s best responses. Taking the derivative with respect to τ and setting to zero

10Note: since the level of τ does not impact state variables, each actor considers only the current periodwhen determining contribution schedules.

11For instance, SIG 2 could provide a schedule that includes lower or higher than truthful contributionsfor some tariff that is not chosen in equilibrium, so long as this is not enough to induce either Government tochoose it or SIG 1 to change their strategy in anticipation of this schedule. Either of these changes would breakthe equilibrium, as SIG 2 would then want to divert to a truthful schedule (in the case of induced changes bySIG 1, this means the schedule would not be commitment credible for SIG 2).

12Technically, this describes an infinite set of subgame perfect strategies, but all of these strategies share aset of properties that makes them indistinguishable in terms of how they effect the outcome. For instance, SIG1 could easily choose a contribution schedule that offers zero contributions for anything but their preferredtariff rate; given that their preferred tariff rate will be chosen in equilibrium.

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returns the following first order condition.

∂u1(τ,St|T = 1,R = 0)∂τ

= ∂π1

∂τ+ψs

(α∂W∂τ

+β∂π2

∂τ

)= 0

This implicitly characterizes an optimal τ∗, when τ∗ is at an interior solution. A cornersolution of τ∗ = 0 is obtained when the above partial derivative is negative at τ = 0, givenstrict concavity and monotonicity assumptions, i.e. when:

∂u1(τ,St|T = 1,R = 0)∂τ

(τ= 0)= ∂π1

∂τ(τ= 0)+ψs

(α∂W∂τ

(τ= 0)+β∂π2

∂τ(τ= 0)

)< 0

We can now derive the comparative statics to determine how τ∗ changes with ε and β usingthe implicit function theorem. This leads to the following proposition.

Proposition 1. The tariff rate chosen by SIG 1 (τ∗) is weakly decreasing in β and ε, i.e.∂τ∗∂β

≤ 0 and ∂τ∗∂ε

≤ 0, and is strictly decreasing when τ∗ is at an interior solution.

Proof in the appendix. These comparative statics should be familiar to those who have readGrossman and Helpman (1994). They provide a good baseline for thinking about the movingparts in this paper, before dynamics are introduced. The intuition is that increases in ε andβ both increase the costs to government from a tariff that SIG 1 has to compensate themfor, either by increasing the welfare costs of that tariff (with ε) or by increasing the degreeto which competing groups oppose the tariff (with β), leading to more foregone contribu-tions from these groups. Substantively, a corner solution is when protection is too costly orthe interest group is too politically weak for any positive tariff rate to be profitably obtained.

However, to generate insights about the choice between protectionism and compensation,we need to understand how the indirect utility function γ(ε,β,ρ,St|T = 1) ≡ u∗

1(τ∗,St|T =1,R = 0) changes with these parameters. I derive these comparative statics as well.

Lemma 1. The single-period indirect utility function γ is weakly decreasing in β and ε when-ever SIG 1 pursues protection, i.e. ∂γ

∂β (T = 1) ≤ 0 and ∂γ

∂ε (T = 1) ≤ 0, and is strictly decreasingwhen τ∗ is at an interior solution.

These comparative statics are fairly intuitive given Proposition 1, and are proven in theappendix. As ε and β increase, obtaining higher tariffs becomes more costly, making tariffsa less attractive means of obtaining transfers from the government.

We can now examine what happens when SIG 1 chooses compensation (i.e. when T = 0). Inthis case, SIG 2 is no longer relevant to the game, as they are indifferent between levels ofcompensation R. Outside of this, SIG 1’s decision problem looks very similar to when theywere determining the optimal tariff rate; they still need to compensate the Governmentfor the welfare costs of compensation, just not for any foregone revenues from SIG 2. Thisproduces the following:

u1(R,St|T = 0,τ= 0)= R+π1(0)−ψs((αW(0,0,ε,ρ)−αW(0,R,ε,ρ))

13

Which leads to the following first order condition:

∂u1(R,St|T = 0,τ= 0)∂R

= 1+ψs

(α∂W(0,R,ε,ρ)

∂R

)= 0

This implicitly characterizes an optimal R∗ when R∗ is an interior solution, and a γ(ε,ρ|T =0)≡ u∗

1(R∗,St|T = 0,τ= 0). A corner solution of R∗ = 0 obtains when:

∂u1(R,St|T = 0,τ= 0)∂R

(R = 0)= 1+ψs

(α∂W(0,R,ε,ρ)

∂R(R = 0)

)< 0

I derive comparative statics in a similar fashion to when protection was chosen.

Proposition 2. The optimal compensation level chosen by SIG 1 (R∗) is weakly increasingin fiscal capacity ρ, as is the single-period indirect utility for when compensation is chosen(i.e. γ(T = 0)). These are strict when R∗ is at an interior solution.

Proof is in the appendix. The intuition here is similar to that of tariffs and import demandelasticities; as fiscal capacity increases, compensation becomes a more attractive instru-ment, leading to higher levels of compensation, and a higher utility from choosing compen-sation. A corner solution of R∗ = 0 is, substantively, the case of uncompensated free trade.

To determine whether SIG 1 would choose compensation or protection in any single period ofthe game, we have to compare the indirect utility obtained when protection or compensationis chosen. Given the assumptions of the model, we have the following:

Proposition 3. In any single period of the game, compensation is weakly preferred to pro-tection, i.e. γ(ε,ρ,β,St|T = 0) ≥ γ(ε,ρ,β,St|T = 1), for all ε, ρ, and β, and compensation isstrictly preferred except when R∗ = 0.

The proof of this is in the appendix, but the intuition is immediately clear. Compensation issimply a less costly way of obtaining transfers from the government, both in welfare terms(it is less distortionary), and because it does not require compensating for foregone contribu-tions from SIG 2. Since it is less costly, in any single period SIG 1 will be able to profitablyobtain more of it, and their indirect utility will be correspondingly higher. This is, in effect,a statement of the puzzle around which this paper is framed: why would an interest groupchoose protection when compensation is less costly?

This also leads to the following useful lemma.

Lemma 2. In any single period of the game, if R∗ = 0 then τ∗ = 0 as well.

Proof of this is in the appendix. The intuition is clear; since R is a more efficient means oftransferring income, if an interest group cannot obtain any rents via R, they will also beunable to obtain any via τ.

We also need to derive comparative statics with respect to ψs, which captures the politicalinfluence of SIG 1. This will be important when dynamics are introduced into the model.

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Proposition 4. The optimal tariff rate τ∗, optimal amount of compensation R∗, and thesingle-period indirect utility function γ are weakly decreasing in political influence ψs, i.e.∂τ∗∂ψs

≤ 0, ∂R∗∂ψs

≤ 0 and ∂γ

∂ψs≤ 0, and are strictly decreasing except in cases of corner solutions.

Proof is in the appendix. The intuition is that as political influence decreases, described hereas an increase in the cost of lobbying contributions/activity, the ability to obtain any kind offavorable policy decreases, reducing the indirect utility obtained from either instrument.

With this in hand, we can now consider the dynamic setting outlined in the setup to themodel. To simplify the exposition, I introduce the following notation:

• χP (ε,β,ψP )= γ(ε,ρ,β,St = P|T = 1)

• χF (ε,β,ψF )= γ(ε,ρ,β,St = F|T = 1)

• φP (ρ,ψP )= γ(ε,ρ,β,St = P|T = 0)

• φF (ρ,ψF )= γ(ε,ρ,β,St = F|T = 0)

χP and χF give the single period indirect utility obtained from tariffs in protectionist andfree trade states respectively. φP and φF give the single period indirect utility obtainedfrom compensation in protectionist and free trade states respectively. From Proposition 3,we know that φP > χP and φF > χF (except when R∗ = 0). This leads to the following lemma:

Lemma 3. In a free trade state, compensation is always chosen over protection.

Proof is immediate. This follows from the fact that φF > χF , and the fact that St = F is anabsorbing state; there is no possibility of exiting the state, and thus no possible advantageto choosing tariffs, given that tariffs lead to a lower level of transfers than compensation.13

Furthermore, given thatψF >ψP , Proposition 4 implies that χF ≤ χP and φF ≤φP , and theseinequalities will all be strict except in cases of corner solutions. Given the dynamic setupoutlined earlier, we can thus consider the following pure strategy Markov (state-dependent)strategies for SIG 1, having ruled out choosing protection in free trade states in Lemma 3.

• σ1 = (T = 0 if St = P,T = 0 if St = F)

• σ2 = (T = 1 if St = P,T = 0 if St = F)

With σ1, SIG 1 chooses compensation in either state of the world. Thus, after the firstround, the state transitions from protectionism (St = P) to free trade (St = F). With σ2, SIG1 chooses protection when in a protectionist state, which maintains their political influencein future periods. SIG 1 would choose compensation if they were in a free trade state, butgiven σ2, they never reach one. These two strategies produce the following value functions,which describe the discounted present value of each strategy, with discount factor δ.

13Technically, when R∗ = 0 and τ∗ = 0, an interest group will be indifferent between protection and compen-sation. However, in this case the instruments are identical, so for simplicity I rule out protection.

15

• V1(σ1)=φP +δ φF

1−δ

• V1(σ2)= χP

1−δ

φP is the single period payoff obtained from pursuing compensation in a protectionist state,δφF

1−δ is the value of the discounted infinite stream of compensation payoffs obtained after

the state transitions to free trade, while χP

1−δ is the value of the discounted infinite stream ofprotection payoffs. SIG 1 prefers to adopt strategy σ1 whenever V1(σ1) > V1(σ2), prefers σ2

when the inequality is reversed, and is indifferent when they are exactly equal. This allowsus to come to the following conclusion.

Proposition 5. The unique Markov Perfect Equilibrium of the model is:

1. If φP +δ φF

1−δ > χP

1−δ , SIG 1 chooses T = 0 in stage 1 of the first period of the game. SIG1 sets a contribution schedule, then obtains a compensation payoff φP . The state thentransitions to free trade, and SIG 1 obtains a payoff of φF for all future periods, withSIG 2 obtaining u2 = X +βπ2(0) in all periods of the game, and Government obtainingC1(0,R∗(St = P))+αW(0,R∗(St = P),ε,ρ) in the first period and C1(0,R∗(St = F)+αW(0,R∗(St = F),ε,ρ) in all subsequent periods.

2. If φP +δ φF

1−δ < χP

1−δ , SIG 1 chooses T = 1 in stage 1. SIG 1 and SIG 2 set contributionschedules, the government chooses τ∗, and the game repeats indefinitely. In every periodof the game, SIG 1 obtains a payoff of χP , SIG 2 gets u2 = X +βπ2(τ∗), and Governmentgets C1(τ∗(St = P),0)+αW(τ∗(St = F),0,ε,ρ).

3. If φP +δ φF

1−δ = χP

1−δ , SIG 1 can randomize between strategies, allowing for a number ofprotectionist states followed by a transition to free trade and compensation thereafter.

Proof follows from preceding discussion. This is the core result of the model. Despite thefact that SIG 1 prefers compensation to protection in any single period of the game (seeProposition 3), they will still often choose to lobby for protection instead, since this allowsthem to retain their political influence and potentially obtain higher rents (if φF < χP ) infuture periods. Thus, the puzzle outlined in the introduction to this paper is resolved byintroducing dynamics. Interest groups cannot obtain their preferred outcome of high levelsof compensation in perpetuity, because the resultant reduction in their political influence re-duces the incentives of Government to accommodate them; the bargaining process betweenSIG 1 and the Government is subject to a commitment problem.

If φF > χP , then the outcome will always be equilibrium 1; this is because even with reducedinfluence in future periods, SIG 1 is still obtaining a higher payoff from compensation thanthey would obtain from pursuing protection in any state. This could, conceivably, be the casefor industries where protection is very “expensive” for an interest group to “purchase” (e.g.if it’s a highly elastic commodity for which there exist powerful downstream lobbies) and if

16

ψF →

Compensation

Protection

ρ ↑

Figure 1: Comparative Statics for ρ (fiscal capacity) and ψF (dynamic decline).(Holding fixed ε, β, and ψP )

the degree of dynamic decline is relatively small (ψF is relatively low).

However, I expect that in most cases, φF < χP , i.e. import-competing SIGs will experience adecrease in rents extracted from the government after liberalization reduces their politicalinfluence. In some cases, you even see the total dissolution of the interest group in questionafter liberalization: this would lead to a very high ψF , and a very low φF . In this case, youmay still get compensation instead of protection, so long as φP > χP

1−δ −δφF

1−δ . In other words,compensation will still be chosen over protection if the single-shot benefit SIG 1 can obtainin the current period exceeds the difference between the discounted stream of tariff payoffsand the discounted stream of reduced-influence compensation payoffs.

Now recall the comparative statics identified earlier in Lemma 1 and Proposition 3, i.e.∂χP

∂ε≤ 0, ∂χ

P

∂β, ∂φ

P

∂ρ≥ 0, ∂φ

F

∂ρ≥ 0, and ∂φF

∂ψF≤ 0. Through the effects these parameters have on χP ,

φF , and φP , we can determine the following:

Proposition 6. Higher import demand elasticities, lobby competition, and fiscal capacityall increase the likelihood that compensation will be chosen as an alternative to protection,while a higher degree of dynamic decline increases the likelihood of protection.

Proof follows from preceding discussion. The intuition of this proposition is that higher im-port demand elasticities and lobby competition increase the cost of protection, while higherfiscal capacity reduces the cost of compensation. A higher degree of dynamic decline reducesthe payoffs to the interest group once free trade has been enacted, reducing their incentiveto accept liberalization.

At this point, it is worth specifically considering the implications of the corner solutions ofτ∗ = 0 and R∗ = 0, as these are substantively interesting, albeit technically complicating. Ifτ∗ = 0 when the state of the world is protectionist (St = P), then the outcome will be free

17

ψP →

Protection

Compensation

UncompensatedFree Trade

ρ ↑

Figure 2: When Do We Get Uncompensated Free Trade?The effects of ρ (fiscal capacity) and ψP (costs of lobbying in protectionist state).

(Holding fixed ε, β, and ψF )

trade, as any amount of compensation will strictly dominate. If R∗ = 0 when St = P, wehave the case of uncompensated free trade; the interest group is not influential enough toobtain either compensation or protection in either state of the world, so free trade is pursuedas a default, leading to payoffs of π1(0) in all periods. Once a corner solution is obtained,further movement in the parameters of the model do not lead to any additional changes inthe equilibria. However, we can assess the impact of the parameters on the likelihood thatsuch a corner solution will be the outcome, which leads to the following proposition.

Proposition 7. Increases in ε and β increase the likelihood of a corner solution of τ∗ = 0,decreases in ρ increase the likelihood of a corner solution of R∗ = 0, and increases in ψsincrease the likelihood of both corner solutions.

Proof is in the appendix. The most substantively interesting case described by this propo-sition is that of uncompensated free trade (R∗ = 0); this paper has focused on the choicebetween protection and compensation, but empirically, we observe many cases of interestgroups receiving neither. The model suggests this is most likely when an interest groupstarts the game off in a relatively weak position (ψP is high) or when fiscal capacity (ρ) islow. ψP could be high for a number of reasons; for instance, an interest group might nothave successfully overcome the collective action problems associated with lobbying the gov-ernment, or might not be located in a politically important geographic area.

We can now identify the conditions under which compensation can make liberalization pos-sible when it otherwise would not be. We have the following proposition:

Proposition 8. Free trade is achieved because of the existence of compensation when bothχP

1−δ < φP +δ φF

1−δ and τ∗(St = P) 6= 0. If τ∗ = 0 when St = P, free trade would have been the

18

ε→

Protection

Compensation Leads to Free Trade

Compensation NotNecessary for

Free Trade

β ↑

Figure 3: When Does Compensation Lead to Free Trade?The effects of β (lobby competition) and ε (import demand elasticity).

(Holding fixed ρ, ψP , and ψF )

outcome anyway, with or without compensation. When, χP

1−δ > φP +δ φF

1−δ , compensation hasno effect on the outcome, as it is not chosen.

Proof is immediate. This follows because SIG 1 always has the option of not pursuing a tariffand achieving a payoff of π1(0) (i.e. if τ∗ = 0), in which case they accept free trade ratherthan engaging in any lobbying activity. If, however, τ∗ 6= 0 when St = P, then lobbying andobtaining a tariff is profitable for SIG 1, and they will do so if that is the only option avail-able to them. However, so long as that payoff is less than what they get from compensation,they will deviate to compensation instead.

This provides theoretical foundations for determining when compensation can be an impor-tant part of a bargain obtaining free trade, instead of something that interest groups will usewhen it’s available but which does not change the outcome. Embedded liberalism suggeststhat compensation is an important part of the political story of liberalization: this modelgives conditions under which this is true, namely that fiscal capacity is sufficiently high tomake compensation an attractive option, and import demand elasticities and lobby competi-tion are high enough to keep protection from being more attractive than compensation, butlow enough that free trade would not be chosen without compensation (See Figure 3).

Other Forms of Political Competition in TradeThe model frames political competition over trade as between industry-level interest groups,with some groups upstream in a production process while others are downstream. This char-

19

acterizes a significant portion of trade politics, but there are two other forms of competitionthat the model can speak to that are worth flagging explicitly: (1) competition between ex-porters and import-competitors; (2) firm-level competition over particularistic trade policies.

To start, much of trade liberalization occurs in the context of reciprocal trade commitmentsmade under some broader trade agreement. In this environment, the set of actors impactedby retaining a protectionist policy expands; export industries that want increased access toforeign markets are pitted directly against import-competing industries that might want toretain protection, and even within an industry, you have competition between firms thatexport and firms that do not (Osgood 2017). This can be incorporated into the model fairlystraightforwardly: it would simply increase the value of β, i.e. the parameter reflecting thedegree of political competition.

However, we also see that in cases of very high levels of product differentiation, tariff codescan become sufficiently fine-grained so as to make protection a particularistic good, cap-tured by only one or a very small number of firms (Kim 2017). Under these conditions, wewould expect lobbying to occur at the firm level (Bombardini and Trebbi 2012), and the un-derlying economic model we can use to understand the situation differs somewhat from thecomparative-advantage framework that has been the focus in this paper.

This too can be understood through the lens of this model. To start, if protectionist policiesoperate at the firm level, then much of the costs of trade protection will arise because ofthe misallocation of resources across firms: indeed, for trade in industries characterized byhigh product differentiation, much of the gains from more open trade have arisen from areallocation of production from less productive to more efficient firms14, while particularis-tic policies have been shown to produce significant welfare costs when they result in firmsgrowing bigger than they should be, leading to a less efficient allocation of labor, capital,and other factors of production (Huneeus and Kim 2019).

Given this, we still have the fundamental dilemma described earlier in this paper: tradeprotection produces welfare costs due to a misallocation of resources, and any compensatorypolicy that allows the gains from trade to be realized by reallocating these resources will re-sult in a reduction of political influence in the groups that favor protectionism. In this case,protection-seeking firms know that losing protection means they will shrink in size, loseprofits, and lose employees, all of which is strongly associated with firm-level political influ-ence (Bombardini 2008, Osgood et al. 2016, Osgood 2017). So as with industry-level trade,the dynamic story remains the same: protectionist firms could be bought with compensatorypolicies, but firms are wary of accepting these due to the reductions in future political influ-ence they are tied to, and thus will only accept them in cases where the prospective decline

14This additional source of gains from trade has been one of the key insights of the heterogeneous firms intrade literature, or “New New Trade Theory”. Trefler (2004) finds that the gains from exiting inefficient pro-ducers accounts for half of the productivity gains from the Canada-US Free Trade Agreement. More broadly,Melitz and Trefler (2012) provide a review of work on gains from trade when firms matter.

20

is limited (which would plausibly occur in cases of more limited product differentiation), orin cases where the costs of pursuing protection are especially high (i.e. when the resourcemisallocation costs are especially high).

RobustnessThe model as outlined makes a number of simplifying assumptions to ensure tractability,and to allow for a cleaner exposition of the main results. An appendix addressing the robust-ness of the results to relaxing these assumptions can be found online, which includes: (1) adiscussion of the sequencing of the game within any period; (2) a discussion of the choice tomodel lobbying as an auction in which interest groups bid to buy policy; (3) a version of themodel in which free-trade is not a fully absorbing state, but one in which interest groupscan regain some (but not all) of their lost political power by lobbying to reimpose protection.This analysis suggests that the core results are not dependent on the particular structureof the model, and the alternative version of the dynamic model produces some interestingnew empirical implications, which are also discussed in the appendix.

Applications of the ModelThis paper was designed to accomplish two goals. First, it has sought to provide an answerto a theoretical puzzle about trade protection: why is it used over more efficient means ofredistributing income? Second, it has looked to provide a theory of compensation in tradepolitics, including when and how compensation can be a useful part of a bargain obtainingfree trade. In pursuit of the second goal, the model has produced clear empirical implicationsthat can be a useful lens for examining the real world use of protection and compensation.

To start, compensation should play an important role in trade politics, but we would expectthe bulk of compensation to come in the form of temporary measures that help cover thedifference in costs to a special interest group between lobbying to maintain tariffs and ad-justing to the costs of more open trade. Long-term measures, in which governments providecontinued support to members of interest groups who lost out from open trade, should berare due to commitment problems in the lobbying process.

In fact, most compensatory policies we observe appear to follow this pattern. Trade Adjust-ment Assistance (TAA) in the United States provides support to those hurt by exposure totrade in the form of job training, wage supplements, and income support, but these ben-efits can only be claimed for a period of about two years (Collins 2014). Similarly, activelabour-market policies (ALMP) popular in several countries in Europe are a collection oftemporary measures including job-training, job search assistance, and the creation of short-term public-sector jobs for the recently unemployed (Bonoli 2010, Vlandas 2013).

21

Table 1: What Makes Each Outcome More Likely?

Protection Compensation Uncompensated Free TradeLow ρ (fiscal capacity) High ρ (fiscal capacity) Low ρ (fiscal capacity)Low ε (elasticity) High ε (elasticity) High ψP (low initial political power)Low β (lobby competition) High β (lobby competition)High ψF (dynamic decline) Low ψF (dynamic decline)

However, while the model predicts compensation will often be an important tool that gov-ernments can use to achieve political bargains on open trade, it also suggests that thesebargains will not be possible in many cases. This should lead to industry strongholds, whereprotection is retained indefinitely, despite its inefficiency. We see plenty of examples of thisas well: for instance, in the United States, sugar, dairy, canned tuna, and footwear are obvi-ous cases. Footwear is discussed in depth later in this paper.

Finally, we should expect the variation in these outcomes (i.e. temporary compensation ver-sus indefinite protection) across industries and countries to be explained by parametersidentified by the model. The impact of these parameters is summarized in Table 1.

The Steel IndustryWe can also examine specific cases of protection and compensation through the lens of themodel. For instance, consider the steel industry in the United States. US Steel is a highlyelastic commodity15 with many powerful downstream interests (Blonigen 2016).

However, steel is also a case where the anticipated degree of dynamic decline of the in-dustry has shifted over time due to the development of a new production technology: min-imills. Minimills drastically increased the productivity of the steel industry, and are farmore capital-intensive than traditional steel production processes.16 Prior to the adventof minimills, the steel industry faced a very steep prospective decline if steel were liberal-ized, and lobbied hard (and successfully) to obtain protection via voluntary export restraints(VERs) and comprehensive quotas at several points. However, as minimills became moreprominent around the late 1980s to early 1990s, this prospective decline became less se-vere: increased foreign competition would decrease the competitiveness of steel producedvia traditional “vertically integrated” processes, but the industry could survive by shiftingmore of their production towards minimills (Collard-Wexler and Loecker 2015).

What was the seeming consequence of this shift in the degree of dynamic decline (ψF )? Asa VER Agreement neared expiry in 1992, steel firms gave up on lobbying for an extension

15Import demand elasticity estimates in Kee, Nicita, and Olarreaga (2008) provide an average elasticity of-3.32 across steel tariff categories , compared to a median of -1.39 across all tariff categories in the US. Thisputs steel at approximately the 78th percentile in the US.

16Collard-Wexler and Loecker (2015) discusses minimills development in detail.

22

(Moore 1996 p. 28). In the 27 years since, while the steel industry has sometimes lobbied forlimited forms of protection, generally via anti-dumping and safeguard provisions in tradelaw, they have given up on ambitions of the more comprehensive protection of the 1970s and1980s. Their more limited demands have rarely been met for long: Bush’s 2002 steel tariffswere reversed quickly under pressure from the EU, and as of writing this, even PresidentTrump has agreed to lift tariffs imposed on steel from Canada and Mexico.17

Meanwhile, during this period, the steel industry has been one of the main recipients oftrade adjustment assistance (TAA), which has often been explicitly marketed politically asa partial solution to the industry’s concerns. For instance, a 2015 statement from MinnesotaGovernor Mark Clayton and Senators Klobuchar and Franken explicitly claimed credit forTAA approval for steel workers, suggesting it came as a result of phone calls they made tothe Department of Labor (Clayton, Franken, and Klobuchar 2015).

Thus, this case follows the predictions of the model almost exactly. High elasticities anddownstream competition made protecting steel fairly costly for the government, but whenthe steel industry was faced with a steep economic decline they were willing to invest thelobbying activity required to obtain it. When a shift in the degree of dynamic decline oc-curred in the late 1980s to early 1990s, this disrupted that equilibrium, leading to a shifttowards compensation and liberalized trade in steel. However, because the degree of dy-namic decline was (relatively) modest, the industry has remained somewhat politically in-fluential, able to obtain compensation and some other temporary concessions, but with aclearly observable reduction in their influence from several decades ago. Moreover, while itis impossible to know for certain what the outcome would have been otherwise, compensa-tion has been treated by politicians as an important part of the political bargain that madeliberalized trade in steel feasible.

The Footwear IndustryThe footwear industry retains some of the highest import tariffs in the United States, at aneffective rate of 9.8% - the highest of any manufactured good (USITC 2011). At the sametime, it is an industry in which the vast majority of domestic consumption is satisfied via im-ports - 98%, worth 26 billion dollars each year (USITC 2015)! Thus, while these tariffs costconsumers billions of dollars each year via increased costs of footwear, the domestic footwearindustry being protected is actually very small, employing only about 12,000 workers.

The most prominent company in this domestic industry is New Balance Athletics. NewBalance has been extraordinarily active in lobbying government officials to maintain thesetariffs, often leveraging their manufacturing facilities in Maine, which employ a few thou-sand workers in the state. This lobbying became especially politically contentious in April2016, when it became clear that the Trans-Pacific Partnership (TPP) was likely to liberal-

17Washington Post, 17 May 2019.

23

ize (on a delayed schedule) import tariffs on Vietnamese footwear. New Balance successfullylobbied both Maine Senators (Susan Collins and Angus King) to oppose the TPP, with AngusKing explicitly linking his opposition to the TPP to New Balance, saying in a statement that“if the TPP, when finalized, does not adequately address the needs of US athletic footwearmanufacturers it would be very unlikely that I would support its passage.” (King 2013).

This lobbying effort became even more contentious on November 10, 2016, when the NewBalance vice president of public affairs made a statement to the Wall Street Journal inwhich he claimed “The Obama administration turned a deaf ear to us and frankly, withPresident-elect Trump, we feel things are going to move in the right direction”, later clarify-ing that this was in reference to Trump’s opposition to the Trans-Pacific Partnership.18 Thiswas taken by white supremacists as a statement of support, leading them to champion theshoes as the “Official Shoes of White People”, which eventually led to a statement by NewBalance denying any association with bigotry.

Given that New Balance’s statement of support for President Trump was made in the im-mediate wake of an exceptionally contentious election, it entailed significant costs for themin terms of public relations, with many speculating that they might have been better servedby keeping quiet. However, one should consider their actions as part of a continued effort tolobby against the TPP, which Trump later withdrew from on January 23, 2017.

To summarize, New Balance invested an extraordinary amount to lobby the governmentagainst reducing footwear tariffs. However, strikingly, New Balance actually produces 75%of their shoes abroad and imports them into the United States, such that the majority oftheir production is subject to the kinds of tariffs they lobbied so hard against.19 It is thusunclear how much footwear tariff reductions would impact them financially. Why, then,would they lobby so actively against them?

The model of this paper can provide insight into this question. The US footwear industry isclearly characterized by low import demand elasticities, given that high tariffs have not keptforeign exporters from obtaining a 98% market share. Furthermore, while large companieslike Nike (which imports all of its footwear from manufacturing facilities abroad) lobbiedfor the tariff reductions, these companies were able to pass off some share of the costs of thetariffs to consumers, and also had a number of other lobbying priorities, such as intellectualproperty and domestic taxation. Thus, the lobbying costs for New Balance of maintainingfootwear tariffs were not as high as one might initially expect.

While eliminating import tariffs would not significantly hurt New Balance’s profits directly,it would eliminate the competitiveness of their US manufacturing operations in Maine, suchthat they would have to shift production overseas. This would significantly reduce New Bal-

18Wall Street Journal, 10 November 2016.19Wall Street Journal, 30 September 2014.

24

ance’s political influence in the future, given how effectively they had leveraged these facto-ries in their past lobbying activities. Consequently, this provides a clean example where apolicy change would bring about a reduction in influence without much affecting profits orother parts of the interest group’s objective function.

How might New Balance use continued political influence to their gain? On November 30,2016, Senators Collins and King announced that they had insured that a provision wouldbe included in the National Defense Authorization Act of 2017 that would require the USmilitary to buy 125,000 pairs a year of New Balance shoes (King 2016). This is essentially apure political rent, and it was obtained because New Balance retained its political influenceby keeping its US manufacturing alive via tariffs on footwear.

Thus, this case illustrates several aspects of this paper’s model: how low import demandelasticities (ε) and lobby competition (β) can make trade tariffs less costly for the govern-ment to provide (even when the costs to consumers seem high), and how high prospectivereductions in political influence (high ψF ) can motivate interest groups to pursue protectionin order to retain political influence in the future.

More generally, the examples of footwear and steel illustrate something broader about thepolitics of trade. In the rationalist conflict literature, the realization that the actors in-volved were not choosing between war and the status quo but between war and negotiatedbargains led to a shift in focus in empirical analysis to the characteristics resulting in bar-gaining breakdown: primarily commitment problems and information asymmetries. In asimilar fashion, this paper’s model leads one to focus on the characteristics blocking com-pensatory alternatives to protection in explaining trade policy patterns: namely, dynamiceffects, and the resulting commitment problems. Indeed, it is unlikely that the standardpolitical economy account would predict that steel, a large and powerful industry, wouldlargely lose protection while the tiny domestic footwear industry would achieve some of thehighest levels of it, but a focus on dynamic considerations can help to resolve this puzzle.

ConclusionThis paper has developed a dynamic model that can help to address two outstanding puzzlesin the political economy of trade literature: (1) Why is trade protection often used by gov-ernments despite the fact that it is an inefficient means of redistributing income? (2) Giventhat both protection and compensation appear to be used by governments, what accountsfor their heterogeneous use across states, sectors, industries, and time? With respect to thefirst puzzle, the model identifies how the dynamic effects of liberalization on the strength ofcompeting lobby groups can lead to instances where protectionism - though less efficient -may be preferred by lobby groups because the Pareto superior compensation transfers aresubject to a commitment problem.

25

With respect to the second puzzle, the model provides a theoretical framework in whichgovernments would be expected to employ both compensation and protection, and providesconditions circumscribing their use, depending on parameters such as import demand elas-ticities, downstream lobby competition, the anticipated degree of dynamic decline, and fis-cal capacity. This can provide insight into both the empirical patterns of compensation andprotection, and the conditions under which compensation is actually pivotal in producingliberalization, allowing for a new interpretation of the compromise of embedded liberalism.

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Appendix for Protection as a Commitment Problem

SequencingIt is worth addressing whether or not the sequencing of the game within any period mattersfor the outcome. I assume that SIG 1 sets their contribution schedule first and thus gets afirst-mover advantage to essentially determine the eventual tariff rate that is implemented(subject to needing to pay for the additional costs to Government). There are two reasonsto believe this assumption is unobjectionable. First, this sequencing seems to approximatewhat trade politics often looks like: industry groups that oppose tariff increases rarely beginlobbying before the protectionist interest group begins advocating for a tariff, and insteadseem to behave in a more reactive fashion. In the case of the steel industry, for instance,steel interest groups have often initiated lobbying for a tariff, with automobile manufactur-ers responding afterwards with their own lobbying activity against it. It is thus reasonableto assume protectionist groups may be able to structure their initial demands in order toobtain some advantage.

However, a much more important response is that while the sequencing is very importantfor the distribution of the surplus from the bargaining process, it should have minimal effecton the policy outcomes generated by this process. Note that if the model produces a positiveτ∗ when protection is chosen, it implies that there is some surplus to the bargaining processgenerated by a tariff; the Government is eventually paid for both their weight on the wel-fare costs of the tariff and the costs of the tariff to SIG 2.1 If SIG 2 valued a zero tariff morethan SIG 1 values the higher tariff, they could pay the government the difference and havea zero tariff implemented; a τ∗ > 0 thus implies that this is not the case. This also impliesthat τ∗ is the value of τ that maximizes this surplus, as SIG 1 is taking both SIG 2 and theGovernment’s marginal costs into account.

The main consequence of SIG 1 going first is that they are able to structure their initial offerin a way that they extract the entirety of the surplus available to the two interest groups; forinstance, in a protectionist state, the value of the total surplus is Ω= χP , and is obtained bySIG 1. Now, instead of analyzing a specific alternative model, let’s consider a larger class ofbargaining models that assign bargaining power θ ∈ [0,1] to SIG 1, and 1−θ to SIG 2, such

1This might seem slightly odd, since tariffs are value-destroying, but this occurs because many of thosewho experience the costs of tariffs (e.g. consumers) only enter into the bargaining process via the welfarecomponent of the government’s utility function, which has the effect of downweighting them relative to theinterest groups in the game.

1

that SIG 1 obtains θΩ and SIG 2 obtains (1−θ)Ω. This allows us to generate the followingproposition:

Proposition 9. Any bargaining model that assigns strictly positive bargaining power to SIG1 (i.e. θ > 0) produces the same results as the baseline model.

Proof is in the proofs section of the appendix. The main exception to note here is that ifSIG 1 has no bargaining power at all, then the results could change, because SIG 1 becomesindifferent between all outcomes of the game in all periods. However, as long as they receivesome positive fixed fraction of the surplus in every period, it does not change the trade-offsthey face between different policy options.

The Lobbying ProcessOne might also question the assumptions the model makes about the lobbying process. Thispaper adopts an exchange model approach to the lobbying process, in which contributionsare traded for policies, but there are broadly two other categories of lobbying models thatare discussed in the literature: (1) signaling models (e.g. Austen-Smith and Wright 1992,1994); (2) legislative subsidy models (Hall and Deardorff 2006).

Signaling models posit that SIGs have private information about several factors that arerelevant to legislators, such as the levels of constituency support for a particular policy, butthese SIGs have incentives to misrepresent this private information in order to try to con-vince the legislator to adopt the SIG’s preferred policy. Thus, costly lobbying becomes a wayof signaling credibly this payoff-relevant information to the government.

However, this approach to understanding lobbying provides fewer clues as to which groupsare likely to be able to obtain protection. In many cases with trade, the relevant informationis widely known: it is clear which interest groups benefit and lose from protection, and thatit harms consumers. There is some new work in trade politics that uses signaling modelsto better understand how firms can persuade the government to pursue their legal casesvia international trade institutions (see Brutger 2017), but this work complements, ratherthan substitutes for traditional approaches to understanding lobbying which likely explaina more substantial part of the variation.

Legislative subsidy models argue that rather than trying to change the effective preferencesof legislators, either by offering lobbying contributions in exchange for policy or by providinglegislators with payoff-relevant information, lobbying is often designed to relax the budgetconstraint of legislators who have similar interests. Thus, legislators act “as if” they areworking on behalf of the lobby group’s preferences, when in actuality they are just moreeffectively pursuing their own interests.

While this approach also has some weaknesses when applied to trade politics, it is alsounclear that the policy implications would be very different from those of exchange models.As the authors note, with a diverse set of legislators to choose between, legislators that

2

favor policies that are also favored by powerful SIGs will obtain the greatest subsidies, andwill thus be the most productive in pursuing their agenda. Policy should consequently bebiased towards those who can organize and make campaign contributions, pay professionallobbyists, and finance organizations that support them (Hall and Deardorff 2006 p. 14).In this sense, the predictions about the factors that underlie interest group influence areessentially the same, suggesting few differences in the predictions generated by adoptingsuch a model instead of an exchange model like the one employed by this paper.

Alternative Dynamic Model:Non-Absorbing LiberalizationDo the core intuitions of the model hold if an interest group can partially regain some oftheir political influence by lobbying for protection in a free trade state, even if they areunable to fully reverse the process? This section introduces a model where this is possi-ble, which produces some new interesting equilibria, but which fundamentally retains thetrade-off of higher net returns from compensation but with dynamic reductions in influencethat drives the results in the version of the model in the main paper.

To do this, let’s consider a variant of the model where there are three states of the world- St ∈ F, M,P - where in addition to the free trade and protectionist states of the worldfrom the main model, we add in a “moderate” state where a group is able to regain someof their political influence after free trade is realized by pursuing protection. So we haveψF >ψM >ψP , with state transitions handled as follows:

• If St = P and compensation is chosen, then the state transitions to St = F. If protectionis chosen, then the states remains St = P.

• If St = F and compensation is chosen, then the state remains St = F. If protection ischosen, then the state transitions to St = M.

• If St = M and compensation is chosen, then the state transitions to St = F. If protec-tion is chosen, then the state remains St = M.

So, once liberalization has occurred from the initial state St = P, it is impossible to returnto that state, but some amount of political influence can be regained by pursuing protectionin a free trade state. The rest of the model remains identical to that found in the main text.

With this in hand, we can now consider all possible Markov strategies for SIG 1, where wedefine such a strategy as a triple:

σi = (l, j,k)= (T = l|St = P,T = j|St = M,T = k|St = F)

In other words, each strategy chooses protection or compensation for each possible state ofthe world. We have the following eight strategies:

1. σ1 = (0,0,0) - Always liberalize

3

2. σ2 = (0,1,0) - Always liberalize unless St = M

3. σ3 = (0,0,1) - Liberalize, then alternate

4. σ4 = (0,1,1) - Liberalize at first, then always protect

5. σ5 = (1,0,0) - Protect, but liberalize off the path

6. σ6 = (1,0,1) - Protect, but mix of liberalize and protect off the path.

7. σ7 = (1,1,0) - Protect, but mix of liberalize and protect off the path.

8. σ8 = (1,1,1) - Always protect.

To determine the Markov Perfect Equilibria (MPE) of this new version of the dynamic model,we need to determine the conditions under which each of these strategies will be chosen.To start, we can determine the payoffs each strategy achieves for SIG 1, where a numberof these strategies will produce observationally equivalent outcomes, leading to identicalpayoffs. Using the notation from the main paper, where φS is the payoff to compensation inany state S and χS is the payoff to protection in any state S, we get the following:

1. V (σ1)=V (σ2)=φP +δ φF

1−δ

2. V (σ3)=φP +δχF+δφM

1−δ2

3. V (σ4)=φP +δχF +δ2 χM

1−δ

4. V (σ5)=V (σ6)=V (σ7)=V (σ8)= χP

1−δ

σ1 and σ2 produce outcomes that are observationally equivalent to the compensation equi-librium from the original version of the model, while σ5,σ6,σ7,σ8 produce outcomes that areobservationally equivalent to the protectionist equilibrium from the original model. Thus ofthese strategies, only σ3 and σ4 produce new empirical implications relative to the originalmodel. I will start by characterizing these new equilibria, before discussing how the maintrade off between protection and compensation that was the primary subject of inquiry inthe original model is affected by the changes in this version of the model.

Consider first σ3. Central to this analysis will be two conditions that determine whetheror not there is alternation between St = F and St = M, once one of those states is reached.These two conditions can be obtained by conjecturing that the strategy is σ3 = (0,0,1) andthen determining what the payoffs must be in order to make this incentive compatible inevery state.

4

We get the first condition as follows:

φF

1−δ ≤ χF +δφM

1−δ2

↔φF ≤ χF +δφM

1+δ↔φF −χF ≤ δ(φM −φF )[1]

Calling this Condition 1, this is obtained by starting from St = F and determining whetheror not SIG 1 would decide to choose protection instead of compensation under the assump-tion that compensation will be chosen when St = M, leading to alternation between the twostates and periods of protection and compensation. Note that the identical condition canbe obtained from simply determining when V (σ3) ≥ V (σ1) = V (σ2), since these two ways ofthinking about the decision are equivalent.

However, another condition must be jointly satisfied for alternation to be incentive com-patible, namely we must start from St = M and determine whether compensation is a bestresponse, given the assumption of alternation.

χM

1−δ ≤ φM +δχF

1−δ2

↔ χM +δχM ≤φM +δχF

↔ χM −φM ≤ δ(χF −χM)

↔φM −χM ≥ δ(χM −χF )[2]

Similarly, this condition can also be obtained by determining when V (σ3) ≥ V (σ4). So an-other way of characterizing the conditions for alternation is:

V (σ3)≥ maxV (σ1),V (σ4)

Conditions 1 & 2 must be jointly satisfied to allow for alternation between states. Intu-itively, these conditions imply that: [1] the payoff difference between compensation in a“moderate” state and in a “free trade” state is high enough to outweigh the cost of accept-ing the lower payoff obtained from choosing protection in a free trade state; [2] the payoffdifference between protection in a moderate state and in a free trade state is low enough toincentivize taking the higher compensation payoff when in a moderate state. You might, forinstance, have both of these conditions satisfied if an interest group obtains very little viaeither mechanism in a free trade state, so occasionally engages in protection so as to transi-tion things to a moderate state, but also if in that moderate state compensation payoffs aresignificantly higher than protectionist payoffs.

If conditions 1 and 2 are satisfied, we can then determine whether or not liberalizationwould occur in the first period, when St = P. Determining this is a straightforward compar-ison of the payoff from “always protection” in the main model to a payoff of compensationfor one period followed by the discounted alternation payoff, i.e. V (σ6)≤V (σ3) iff:

5

χP

1−δ ≤φP +δ(χF +δφM

1−δ2

)The intuition here is similar to that from the main model, in that in the initial free tradestate SIG 1 is still deciding whether or not to give up some amount of influence permanentlyin exchange for a higher initial compensation payoff. However, the observable implicationsif σ3 is chosen are somewhat different than any equilibrium in the original model: instead,we would expect some amount of influence to be given up in some initial period, followed byalternating cycles of compensation and protection.

In fact, the US steel industry fits better with this version of the model than the originalmodel, as steel has given up some amount of influence and market share since the 1980s,but has experienced alternating cycles of compensation and protection since then. So thisversion of the model can possibly better explain these kinds of cases.

One other new equilibrium which is observably different from those obtained in the earlierversion of the model is σ4 = (0,1,1). In this case, there is liberalization in some initial period,followed by protection every following period. Similarly to σ3, we start by determining whatwould happen following this period of liberalization, where the conditions for things getting“stuck” in St = M can be written as:

V (σ4)≥ maxV (σ1),V (σ3)

Or, breaking this apart into separate conditions:

V (σ4)≥V (σ3)↔ χM +δχM ≥φM +δχF (3)

V (σ4)≥V (σ1)↔φF −χF ≤ δ(χM −χF ) (4)

Condition 3 is simply the reversal of Condition 2 from before, and can be interpreted sim-ilarly: the additional payoff from compensation in the short term (while St = M) has to below enough that it’s not worth it to accept a lower payoff in the subsequent period, whenSIG 1 will be faced with St = F.

Condition 4 ensures that the additional payoff that could be obtained by switching to com-pensation when St = F is less than the additional payoff that could be obtained from pro-tecting in the short term in order to regain some political influence, and then continuing toprotect to retain that influence.

Finally, we need to determine whether liberalization will occur in the first period, i.e. weneed to find where V (σ4)≥V (σ8), which is when:

φP +δχF +δ2 χM

1−δ ≥ χP

1−δThe intuition here is, again, similar to the original model, in that SIG 1 is deciding whetherto give up some amount of influence in the future (characterized by the difference between

6

ψM and ψP ) in exchange for a higher compensation payoff in the short term (i.e. φP ). Themain empirical difference is that the eventual equilibrium is largely one of continued pro-tection, but with some reduction in the level of protection, and some reduction in influencefor SIG 1, relative to the initial period.

A case that fits this especially well is the Canadian dairy industry, which has acceptedbillions of dollars in compensation in exchange for allowing increased access by foreign pro-ducers to the Canadian market as part of various trade agreements, but with that accessremaining sharply limited.2 Interest groups representing Canadian dairy producers havethus been willing to give up some degree of influence and profits in exchange for very highshort term compensation payoffs, but they remain interested in retaining the bulk of theirinfluence.

Finally, we can consider the equilibria that are observationally equivalent to those obtainedin the original version of the model. First, let’s determine the conditions that allow for the“full liberalization” equilibrium of a continuing state of St = F with compensation for SIG1, i.e. strategies σ1 and σ2. Since these strategies produce identical payoffs, we can firstconsider the conditions defined by:

V (σ1)≥ maxV (σ3),V (σ4)

The two conditions generated by this are simply the reversals of conditions 1 and 4 respec-tively. The intuition is similarly straightforward: compensation must be high enough todeter SIG 1 from lobbying for protection to regain influence, where they can use that in-creased influence either to continue to lobby for protection indefinitely, or to obtain a highercompensation payoff after regaining influence, followed by a return to a free trade state(this is the alternation scenario). If neither of these rationales for accepting the short termcosts of lobbying for protection holds, then SIG 1 accepts the long term “full liberalization”outcome.

Having established this, all that remains is to determine whether SIG 1 chooses protectionin the first period, or allows for full liberalization in exchange for the short term compensa-tion at the beginning of the game, i.e. whether V (σ1) ≥ V (σ5). This condition is identical tothat from the original model:

φP +δ φF

1−δ ≥ χP

1−δWith the intuition of this equilibrium being identical to what was discussed in the mainpaper.

For thoroughness, it is worth addressing what determines whether σ1 or σ2 is the equilib-rium strategy; in this case, it depends on whether SIG 1 would rather stay in a protectioniststate if they reached St = M, even though reaching that state is off the equilibrium path.This would be the case if:

2National Post, 20 March 2019.

7

χM

1−δ ≥φP + φF

1−δWe should similarly determine the off-equilibrium-path conditions that distinguish σ5,σ6,σ7,σ8.These, in fact, have been characterized by the earlier parts of this section: when the condi-tions hold for any of the earlier strategies except for the one that compares it to the “alwaysprotect” equilibrium, then those are the strategies that are played off the path. For instance,if conditions 1 and 2 hold, resulting in alternation off the path, but V (σ6) ≥ V (σ3), then wewould have the strategy σ6.

While all these strategies are observationally equivalent, it is useful to distinguish them inorder to think more clearly about the counterfactual which protection is being chosen over.In the case of σ5,σ7, protection in the first period is being chosen over the alternative of fullliberalization and limited compensation going forward. In the case of σ6, protection is beingchosen over a mix of compensation and more limited protection going forward. Finally, withσ8, protection is being chosen over continued protection in the future, but with some reduc-tion in future political influence.

To summarize: in each case, the main trade-off interest groups face is between some degreeof reduced influence in exchange for a higher compensation payoff relative to what they canobtain via protection. However, this new version of the dynamic model produces two sub-stantively different equilibria: one in which after the initial period of liberalization there isa mix of protection and compensation going forward, and one in which there is an initial,partial liberalization followed by continued protection, but at a lower level going forwardthan what was initially obtained. Both of these equilibria have empirical instantiations, inaddition to the “compensate then liberalize” and “protectionist stronghold” equilibria dis-cussed in the original paper.

Proofs of Propositions

Proof of Proposition 1The first order condition characterizing τ∗ is:

∂u1(τ,St|T = 1,R = 0)∂τ

= ∂π1

∂τ+ψs

(α∂W∂τ

+β∂π2

∂τ

)= 0

First, implicitly differentiate the first order condition (for expositional purposes, call this H)with respect to τ.

∂H∂τ

= ∂2π1

∂τ2 +ψsα∂2W∂τ2 +ψsβ

∂2π2

∂τ2

Note that all these terms are negative as a result of earlier concavity assumptions. Next,differentiate H with respect to ε.

∂H∂ε

=ψsα∂2W∂τ∂ε

8

This is also negative, given the assumption made on the conditioning effect of ε. Now, applyimplicit function theorem:

∂τ∗

∂ε=− ψsα

∂2W∂τ∂ε

∂2π1∂τ2 +ψsα

∂2W∂τ2 +ψsβ

∂2π2∂τ2

< 0

Which is, thus, clearly negative. However, if τ∗ = 0, then it is at the bound and cannot bereduced any further. A similar approach is applied to determining the effect of β.

∂H∂β

=ψs∂π2

∂τ

Applying implicit function theorem again returns:

∂τ∗

∂β=−

∂π2∂τ

∂2π1∂τ2 +α∂2W

∂τ2 +β∂2π2∂τ2

< 0

Which is clearly negative given that SIG 2 is a downstream SIG and thus wants lower τ,implying that ∂π2

∂τ< 0. Again, if τ∗ = 0, then it is at the bound and cannot be reduced any

further.

Proof of Lemma 1We have the objective function for SIG 1:

u1(τ,St|T = 1,R = 0)=π1(τ)+ψs(αW(τ,0,ε,ρ)+βπ2(τ)−αW(0,0,ε,ρ)−βπ2(0))

We can determine how the indirect utility function γ(T = 1) = u1(τ∗,St|T = 1,R = 0) varieswith the parameters by applying envelope theorem. Take the simple partial derivative ofthe objective function with respect to each parameter, and then evaluate at the optimum.So for ε, we have:

∂γ

∂ε(T = 1)=ψsα

∂W∂ε

(τ= τ∗)+ψsα∂W∂ε

(τ= 0)

Which since we have assumed in the model setup that ∂W∂ε

(τ= 0)= 0 (i.e. that import demandelasticities only matter to welfare if tariffs are positive) gives us:

∂γ

∂ε(T = 1)=ψsα

∂W∂ε

(τ= τ∗)

This will be negative for any τ∗ > 0, given that we have assumed that ∂W∂ε

(τ)> 0 for any τ> 0.If τ∗ = 0, then the above with be zero, as we have assumed that ∂W

∂ε(τ= 0)= 0.

Similarly, we find the comparative statics for β as follows:

∂γ

∂β(T = 1)=ψs(π2(τ∗)−π2(0))

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Given that ∂π2∂τ

< 0, we know that for any τ∗ > 0, π2(τ∗) < π2(0), such that π2(τ∗)−π2(0) < 0.Thus, for any τ∗ > 0, ∂γ

∂β(T = 1)< 0. However, if τ∗ = 0, then π2(τ∗)−π2(0)= 0, so ∂γ

∂β(T = 1)= 0

as well.

Proof of Proposition 2We have the following first order condition characterizing the optimal R∗.

∂u1(R,St|T = 0,τ= 0)∂R

= 1+ψs

(α∂W(0,R,ε,ρ)

∂R

)= 0

First, implicitly differentiate the first order condition (call this H for expositional purposes)with respect to R.

∂H∂R

=ψsα∂2W∂R2

By earlier concavity assumptions, this is negative. Next, differentiate H with respect to ρ.

∂H∂ρ

=ψsα∂2W∂R∂ρ

Which is positive, given the assumption made about the conditioning effect of ρ. Applyingimplicit function theorem, we get:

∂R∗

∂ρ=−

ψsα∂2W∂R∂ρ

ψsα∂2W∂R2

=−∂2W∂R∂ρ∂2W∂R2

Which is positive, as a result of the above. However, if R∗ = 0, then it is at the lower bound,such that decreases in ρ cannot have any additional effect.

Next, we wish to determine how γ(T = 0) varies with ρ. We have the objective function forSIG 1:

u1(R,St|T = 0,τ= 0)= R+π1(0)−ψs((αW(0,0,ε,ρ)−αW(0,R,ε,ρ))

We use envelope theorem. Take the simple partial derivative with to ρ and then evaluate atR∗:

∂γ

∂ρ(T = 0)=ψsα

(∂W∂ρ

(R∗)− ∂W∂ρ

(0))

Which since it was assumed that ∂W∂ρ

(0)= 0, gives us:

∂γ

∂ρ(T = 0)=ψsα

∂W∂ρ

(R∗)

Which is strictly positive for any R∗ > 0, and is equal to zero at R∗ = 0, by earlier assump-tions.

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Proof of Proposition 3Consider any optimal tariff rate τ∗. We can construct an R that provides the equivalentamount of transfers to SIG 1:

R =π1(τ∗)−π1(0)

Now we can compare the utility obtained from τ∗ and R, taking into account the requiredlobby contributions. In particular, we have:

u1(τ∗,St|T = 1,R = 0)=π1(τ∗)+ψs(αW(τ∗,0,ε,ρ)+βπ2(τ∗)−αW(0,0,ε,ρ)−βπ2(0))

and:u1(R,St|T = 0,τ= 0)= R+π1(0)−ψs((αW(0,0,ε,ρ)−αW(0, R,ε,ρ))

We have constructed R such that it is equal to π1(τ∗)−π1(0), and thus, R+π1(0) = π1(τ∗)−π1(0)+π1(0)=π1(τ∗). Therefore, u1(τ∗,St|T = 1,R = 0)< u1(R,St|T = 0,τ= 0) iff:

αW(τ∗,0,ε,ρ)+βπ2(τ∗)−αW(0,0,ε,ρ)−βπ2(0)<αW(0, R,ε,ρ)−αW(0,0,ε,ρ)

Given that ∂π2∂τ

< 0, we know that π2(τ∗) ≤ π2(0), such that π2(τ∗)−π2(0) ≤ 0. Moreover,by Assumption 1, we know that αW(τ∗,0,ε,ρ)−αW(0,0,ε,ρ) < αW(0, R,ε,ρ)−αW(0,0,ε,ρ).Thus, u1(τ∗,St|T = 1,R = 0) < u1(R,St|T = 0,τ = 0), implying R is preferred to τ∗ in anysingle period of the game.

R thus demonstrates that there exists a compensation level that improves upon τ∗ in anysingle period. By properties of optimality, it must be the case that u1(R,St|T = 0,τ = 0) ≤u1(R∗,St|T = 0,τ= 0)= γ(T = 0).

If τ∗ = 0, then either R∗ > 0, which is preferred, or R∗ = 0, in which case the payoffs to bothprotection and compensation are equal to π1(0).

This completes the proof of Proposition 3.

Proof of Lemma 2Proof by contrapositive. Proposition 3 demonstrates that for any τ 6= 0, there exists anR 6= 0 that is strictly preferred to it. Thus, τ∗ 6= 0 → R∗ 6= 0, which is logically equivalent toR∗ = 0→ τ∗ = 0. This completes the proof of Lemma 2.

Proof of Proposition 4We start by showing that ∂τ∗

∂ψs≤ 0. The first order condition characterizing τ∗ is:

∂u1(τ,St|T = 1,R = 0)∂τ

= ∂π1

∂τ+ψs

(α∂W∂τ

+β∂π2

∂τ

)= 0

First, implicitly differentiate the first order condition (for expositional purposes, call this H)with respect to τ.

∂H∂τ

= ∂2π1

∂τ2 +ψsα∂2W∂τ2 +ψsβ

∂2π2

∂τ2

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Note that all these terms are negative as a result of earlier concavity assumptions. Next,differentiate H with respect to ψs:

∂H∂ψs

=α∂W∂τ

+β∂π2

∂τ

Since ∂W∂τ

< 0 and ∂π2∂τ

by earlier assumption, this is clearly also negative. Thus, by implicitfunction theorem we have that:

∂τ∗

∂ψ=− α∂W

∂τ+β∂π2

∂τ

∂2π1∂τ2 +ψsα

∂2W∂τ2 +ψsβ

∂2π2∂τ2

< 0

The comparative statics are strict unless τ∗ = 0, in which case increases in ψs cannot reduceτ∗ below its lower bound.

Next, let’s show that ∂R∗∂ψ

≤ 0. We have the following first order condition characterizing theoptimal R∗.

∂u1(R,St|T = 0,τ= 0)∂R

= 1+ψs

(α∂W(0,R,ε,ρ)

∂R

)= 0

First, implicitly differentiate the first order condition (call this H for expositional purposes)with respect to R.

∂H∂R

=ψsα∂2W∂R2

By earlier concavity assumptions, this is negative. Next, differentiate H with respect to ψ.

∂H∂ψ

=α∂W(0,R,ε,ρ)∂R

Which is also negative by earlier concavity assumption. Thus, by implicit function theorem,we have:

∂R∗

∂ψ=−α

∂W(0,R,ε,ρ)∂R

ψsα∂2W∂R2

< 0

This comparative static is also strict unless R∗ = 0.

Next, let’s show that both γ(T = 0) and γ(T = 1) are decreasing in ψs. First, we take theobjective function for SIG 1 when T = 1, i.e.:

u1(τ,St|T = 1,R = 0)=π1(τ)+ψs(αW(τ,0,ε,ρ)+βπ2(τ)−αW(0,0,ε,ρ)−βπ2(0))

To find ∂γ

∂ψs(T = 1), we apply envelope theorem to the above, taking the simple partial deriva-

tive with respect to ψs and evaluating at τ∗.

∂γ

∂ψs(T = 1)=αW(τ∗,0,ε,ρ)+βπ2(τ∗)−αW(0,0,ε,ρ)−βπ2(0)

Since ∂W∂τ

< 0 and ∂pi2∂τ

< 0, it must be the case that αW(0,0,ε,ρ)>αW(τ∗,0,ε,ρ) and βπ2(0)>βπ2(τ∗). Thus, ∂γ

∂ψs(T = 1) < 0 at any τ∗ 6= 0. If τ∗ = 0, the above expression is also equal to

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zero.

Similarly, we take the objective function when T = 0:

u1(R,St|T = 0,τ= 0)= R+π1(0)−ψs((αW(0,0,ε,ρ)−αW(0,R,ε,ρ))

Then we apply envelope theorem, obtaining:

∂γ

∂ψs(T = 0)=αW(0,0,ε,ρ)−αW(0,R,ε,ρ)

Which since ∂W∂R < 0, αW(0,R,ε,ρ) > αW(0,0,ε,ρ), which implies that ∂γ

∂ψs(T = 0) < 0, at any

R∗ 6= 0. If R∗ = 0, the above expression is also equal to zero.

This completes the proof of Proposition 4.

Proof of Proposition 7Recall that a corner solution of τ∗ = 0 is obtained when:

∂u1(τ,St|T = 1,R = 0)∂τ

(τ= 0)= ∂π1

∂τ(τ= 0)+ψs

(α∂W∂τ

(τ= 0)+β∂π2

∂τ(τ= 0)

)< 0

To determine the impact of parameters on the likelihood that this will hold, we simply needto find out which parameters decrease ∂u1

∂τ. So we differentiate u1 again with respect to the

different parameters, obtaining the following:

∂2u1(τ,St|T = 1,R = 0)∂τ∂ε

=ψsα∂2W∂τ∂ε

∂2u1(τ,St|T = 1,R = 0)∂τ∂β

=ψs∂π2

∂τ

∂2u1(τ,St|T = 1,R = 0)∂τ∂ψs

=α∂W∂τ

+β∂π2

∂τ

By earlier assumption, we have that ψs > 0, α > 0, ∂2W∂τ∂ε

< 0, ∀τ 6= 0. So the first of these isclearly negative. Similarly, since ψs > 0 and ∂π2

∂τ< 0, the second is negative. Finally, since

α> 0, ∂W∂τ

< 0, β> 0, and ∂π2∂τ

< 0, the third is also negative. Therefore, increases in ε,β andψs all lead it to be more likely that the condition leading to τ∗ = 0 will hold by decreasing ∂u1

∂τ.

Similarly, for compensation we have the following condition leading to R∗ = 0.

∂u1(R,St|T = 0,τ= 0)∂R

(R = 0)= 1+ψs

(α∂W(0,R,ε,ρ)

∂R(R = 0)

)< 0

So we differentiate as follows:

∂2u1(R,St|T = 0,τ= 0)∂R∂ρ

=ψsα∂2W(0,R,ε,ρ)

∂R∂ρ∂2u1(R,St|T = 0,τ= 0)

∂R∂ψs=α∂W(0,R,ε,ρ)

∂R

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Since ψs > 0, α> 0, and ∂2W(0,R,ε,ρ)∂R∂ρ > 0, ∀R 6= 0, the first of these is positive. Since α> 0 and

∂W(0,R,ε,ρ)∂R < 0, the second is negative. So increases in ρ lead to a lower likelihood of a corner

solution of R∗ = 0, while increases in ψs increase the likelihood of R∗ = 0. This completesthe proof of Proposition 7.

Proof of Proposition 9The shift in bargaining power leads to the following new value functions V ′

1(σ1) and V ′1(σ2)

for SIG 1, which we can compare to the original value functions V1(σ1) and V1(σ2)

• V ′1(σ1)= θφP +δθφF

1−δ = θV1(σ1)

• V ′1(σ2)= θχP

1−δ = θV1(σ2)

Thus, V ′1(σ1)>V ′

1(σ2) if and only if:

θV1(σ1)> θV1(σ2)

Which for any θ > 0 is equivalent to:

V1(σ1)>V1(σ2)

This completes the proof of Proposition 9.

ReferencesAusten-Smith, David, and John R. Wright. 1992. Competitive Lobbying for a Legislator’sVote. Social Choice and Welfare 9.3: 229-257.

Austen-Smith, David, and John R. Wright. 1994. Counteractive Lobbying. American Journalof Political Science 38.1: 25-44.

Brutger, Ryan. 2017. Litigation for Sale: Private Firms and WTO Dispute Escala-tion. Working Paper available at: http://web.sas.upenn.edu/brutger/files/2017/02/

Litigation_For_Sale_2-3-17_Full_VERSION-2h4f1bv.pdf

Hall, Richard L., and Alan V. Deardorff. 2006. Lobbying as Legislative Subsidy. The Ameri-can Political Science Review 100.1: 69-84.

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